The Double-Copy Root of Hawking Thermality

Abstract: The Hawking radiation spectrum from a collapsing null shell can be derived via the double copy of a simpler gauge theory calculation. Analyzing the non-abelian Yang-Mills root of this process, we demonstrate that the radiation spectrum is thermal in the color charge eigenvalue $\lambda$, not energy. Considering the $SU(N_c)$ gauge theory in the large $N_c$ limit, we find the differential spectrum $dN/ d\lambda$ is a product of the gravitationally familiar Planck-like factor and the color phase space density, modeled here as the Wigner semicircle from random matrix theory. This reveals that apparent energy thermality in gravity is the direct dual of charge thermality in its underlying non-abelian gauge theory.